Pith Number

pith:PGPSMYEE

pith:2015:PGPSMYEE2JDKVDLTD3RIYSOOPE

not attested not anchored not stored refs pending

Sign patterns of the Liouville and M\"obius functions

Kaisa Matom\"aki, Maksym Radziwi{\l}{\l}, Terence Tao

arxiv:1509.01545 v2 · 2015-09-04 · math.NT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PGPSMYEE2JDKVDLTD3RIYSOOPE}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T01:32:18.212383Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

799f266084d246aa8d731ee28c49ce7928426e7810bd62f663346638f5300ea2

Aliases

arxiv: 1509.01545 · arxiv_version: 1509.01545v2 · doi: 10.48550/arxiv.1509.01545 · pith_short_12: PGPSMYEE2JDK · pith_short_16: PGPSMYEE2JDKVDLT · pith_short_8: PGPSMYEE

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/PGPSMYEE2JDKVDLTD3RIYSOOPE \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 799f266084d246aa8d731ee28c49ce7928426e7810bd62f663346638f5300ea2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5c73fbc6661ff4ab963e3b5f50137e4acfa7bd7abc1925968788bcdd4d1bf600",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2015-09-04T18:04:40Z",
    "title_canon_sha256": "7067f6f78bf4beef2f6a947d53031faeb2da59d0d151f4e843ff377d31a0e404"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.01545",
    "kind": "arxiv",
    "version": 2
  }
}